Inverse transform sampling (also known as inversion sampling, the inverse
probability integral transform, the inverse transformation method, Smirnov transform, ...

Inverse transform sampling

O termo Inverse transform sampling é utilizado na Wikipedia de língua inglesa, onde se pode ler:

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, golden rule, etc.) is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its cumulative distribution function (cdf).

The basic idea is to uniformly sample a number between 0 and 1, interpreted as a probability, and then return the largest number from the domain of the distribution such that . For example, imagine that is the standard normal distribution (i.e. with mean 0, standard deviation 1). Then if we choose , we would return 0, because 50% of the probability of a normal distribution occurs in the region where . Similarly, if we choose , we would return 1.95996...; if we choose , we would return 2.5758...; if we choose , we would return 4.891638...; etc. Essentially, we are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs to the left of that number. Intuitively, we are unlikely to choose a number in the tails because there is very little area in them: We'd have to pick a number very close to 0 or 1.

Computationally, this method involves computing the quantile function of the distribution — in other words, computing the cumulative distribution function (CDF) of the distribution (which maps a number in the domain to a probability between 0 and 1) and then inverting that function. This is the source of the term "inverse" or "inversion" in most of the names for this method. Note that for a discrete distribution, computing the CDF is not in general too difficult: We simply add up the individual probabilities for the various points of the distribution. For a continuous distribution, however, we need to integrate the probability density function (PDF) of the distribution, which is impossible to do analytically for most distributions (including the normal distribution). As a result, this method may be computationally inefficient for many distributions and other methods are preferred; however, it is a useful method for building more generally applicable samplers such as those based on rejection sampling.

For the normal distribution, the lack of an analytical expression for the corresponding quantile function means that other methods (e.g. the Box–Muller transform) may be preferred computationally. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on: see, for example, the ziggurat algorithm and rejection sampling. On the other hand, it is possible to approximate the quantile function of the normal distribution extremely accurately using moderate-degree polynomials, and in fact the method of doing this is fast enough that inversion sampling is now the default method for sampling from a normal distribution in the statistical package R.

Este texto é um excerto do artigo Inverse transform sampling da enciclopédia livre Wikipédia. Na Wikipédia, está disponível uma lista dos autores.

Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, Smirnov transform, golden rule, etc.) is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its cumulative distribution function (cdf).

The basic idea is to uniformly sample a number between 0 and 1, interpreted as a probability, and then return the largest number from the domain of the distribution such that . For example, imagine that is the standard normal distribution (i.e. with mean 0, standard deviation 1). Then if we choose , we would return 0, because 50% of the probability of a normal distribution occurs in the region where . Similarly, if we choose , we would return 1.95996...; if we choose , we would return 2.5758...; if we choose , we would return 4.891638...; etc. Essentially, we are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs to the left of that number. Intuitively, we are unlikely to choose a number in the tails because there is very little area in them: We'd have to pick a number very close to 0 or 1.

Computationally, this method involves computing the quantile function of the distribution — in other words, computing the cumulative distribution function (CDF) of the distribution (which maps a number in the domain to a probability between 0 and 1) and then inverting that function. This is the source of the term "inverse" or "inversion" in most of the names for this method. Note that for a discrete distribution, computing the CDF is not in general too difficult: We simply add up the individual probabilities for the various points of the distribution. For a continuous distribution, however, we need to integrate the probability density function (PDF) of the distribution, which is impossible to do analytically for most distributions (including the normal distribution). As a result, this method may be computationally inefficient for many distributions and other methods are preferred; however, it is a useful method for building more generally applicable samplers such as those based on rejection sampling.

For the normal distribution, the lack of an analytical expression for the corresponding quantile function means that other methods (e.g. the Box–Muller transform) may be preferred computationally. It is often the case that, even for simple distributions, the inverse transform sampling method can be improved on: see, for example, the ziggurat algorithm and rejection sampling. On the other hand, it is possible to approximate the quantile function of the normal distribution extremely accurately using moderate-degree polynomials, and in fact the method of doing this is fast enough that inversion sampling is now the default method for sampling from a normal distribution in the statistical package R.

Este texto é um excerto do artigo Inverse transform sampling da enciclopédia livre Wikipédia. Na Wikipédia, está disponível uma lista dos autores.

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Inverse transform sampling - Wikipedia, the free encyclopedia

Inverse transform sampling (also known as inversion sampling, the inverse
probability integral transform, the inverse transformation method, Smirnov
transform, ...

en.wikipedia.org/wiki/Inverse_transform_sampling

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Inverse transform sampling

Inverse transform sampling, also known as the inverse probability integral
transform or inverse transformation method or Smirnov transform, is a method for
...

www.princeton.edu/~achaney/tmve/wiki100k/docs/Inverse_transform_sampling.html

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1 Inverse Transform Method

1 Inverse Transform Method. Assuming our computer can hand us, upon demand
, iid copies of rvs that are uniformly dis- tributed on (0,1), it is imperative that we ...

www.columbia.edu/~ks20/4404-Sigman/4404-Notes-ITM.pdf

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Lecture 3 Inverse transform method

6 Feb 2002 ... Inverse transform method. • How does one transform a sample of the uniform[0,1]
random variable into a sample of a given distribution ?

www.control.auc.dk/~henrik/undervisning/DES/lec03.pdf

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Inverse Transform Method

Inverse Transform Method for simulating continuous random variables. Let X be a
random variable with c.d.f. FX (x). Since FX (x) is a nondecreasing function, the ...

www.cs.bgu.ac.il/~mps042/invtransnote.htm

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Fast inverse transform sampling in one and two dimensions

4 Jul 2013 ... A classical approach is Inverse transform sampling, in which pseudo- ... [Inverse transform sampling] requires a complete approximation to [the.

arxiv.org/pdf/1307.1223

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Sampling Methods - People.fas.harvard.edu

Page 1. Sampling Methods. Patrick Lam. Page 2. Outline. Inverse CDF Method.
Rejection Sampling. Page 3. Outline. Inverse CDF Method. Rejection ...

www.people.fas.harvard.edu/~plam/teaching/methods/sampling/sampling.pdf

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General Sampling Methods

General Sampling Methods. Reference: Glasserman, § 2.2 and § 2.3. Claudio
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) ...

www.econ-pol.unisi.it/fineng/gensampl_doc.pdf

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An Introduction to Monte Carlo - SLAC

23 Feb 2011 ... Can sample from U(0 ≤ x ≤ 1). Want to sample from any arbitrary probability
distribution f(x). Try Inverse transform sampling. Let F be the ...

www.slac.stanford.edu/slac/sass/talks/MonteCarloSASS.pdf

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Inverse Transform Technique

Inverse Transform Technique. The inverse transform technique can be used to sample from exponential, the uniform, the Weibull and the triangle distributions.

www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node49.html

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Inverse transform sampling na Ciência

Inverse transform sampling - Wikipedia, the free encyclopedia

Inverse transform sampling

Inverse transform sampling, also known as the inverse probability integral transform or inverse transformation method or Smirnov transform, is a method for
...

[PDF]Direct and inverse discrete Zernike transform - ResearchGate

1ICMA, Universidad de Zaragoza and Consejo Superior de Investigaciones ... (
critical) sampling along with an invertible transformation can be useful in a.

[PDF]Tools for sampling Multivariate Archimedean ... - YieldCurve.com

Universidad Nacional del Litoral. Santa Fe - ... proposed an alternative method,
which is computationally more ... is equal to the inverse of the Laplace transform.

Content. Tecnun. Universidad de Navarra.

1.2 Sampling analog signals 1.3 Discrete-time ... 2.4 Inverse Z-Transform
Methods ... 4.3 Relation between the Z-Transform and the Frequency Response

[PDF]inverse sampling and triangular sequential designs to - Idescat

Inverse sampling and formal sequential designs may prove useful in redu- cing
the sample size in ... ratio, angular transform and Sprott's transform). The
expected ... Facultad de Medicina, Universidad Autónoma de Barcelo- na.
Barcelona ...

Direct and inverse discrete Zernike transform - Optics InfoBase

21 Dec 2009 ... The discrete Zernike modes are given for different sampling patterns and ... and
Ricardo Rivera, "Direct and inverse discrete Zernike transform," ...

Advanced Signal Processing. MS-CE 007 - laboratorio en Ingeniería ...

The inverse z-Transform Properties of the z-Transform z-Transforms of LTI
systems. The unilateral z-Transform. Sampling of Continuous-Time Signals

[PDF]UNIVERSIDAD CARLOS III DE MADRID Departamento de Teor´ıa ...

2.4.1 Inverse-of-density method for monotonic pdf's . . . . . 26 ...... The inverse transform method allows to easily generate i.i.d. random numbers from a generic
...

[PDF]Sampling Theorem and Discrete Fourier Transform - REPOSITORIO ...

2Departamento de Matemática Aplicada, Universidad de Murcia, Facultad de ...
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